Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

A
List of Symbols
The table below lists the mathematical symbols that are used throughout this thesis. Other symbols
used less extensively are defined in the text.
Symbol Definition Symbol Definition
ψ Fast S-wave polarisation δV S % Difference in S-wave velocities
δt Time lag between fast and
slow S-waves
δt N Normalised time lag between
fast and slow S-waves
θ S Initial S-wave polarisation ω Seismic wave frequency
θ Arrival azimuth ϕ Arrival inclination
ξ Fracture or microcrack density
γ Thomsen’s parameter
δ Thomsen’s parameter α Fracture strike
µ Lamé parameter λ Lamé parameter
ν Poisson’s ratio ρ Rock density
C Stiffness tensor S Compliance tensor
B N
Normal compliance of a fracture
set
B T
Tangential compliance of a
fracture set
∆S Additional compliance a Fracture aspect ratio
c Fracture aperture r Fracture radius
κ Rock permeability Φ Rock porosity
η Viscosity K Bulk modulus
E Young’s modulus β ijkl 4th order crack density
α ij 2nd order crack density β w Biot-Willis parameter
P fl Pore pressure σ ij Stress tensor
ε Strain tensor σ ′ ij Effective stress tensor
p Mean effective stress q Differential effective stress
τ Shear stress σ n ′ Normal effective stress
K 0 Stress path parameter γ 1 Stress path parameter
γ 3 Stress path parameter χ Cohesion
m Coefficient of friction ϕ f Angle of friction
q crit Fracture critical shear stress f p Fracture potential
187